The grades on a math midterm at Gardner Bullis are normally distributed with $\mu = 82$ and $\sigma = 4.5$. Christopher earned a $90$ on the exam. Find the z-score for Christopher's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Christopher's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{90 - {82}}{{4.5}}} $ ${ z \approx 1.78}$ The z-score is $1.78$. In other words, Christopher's score was $1.78$ standard deviations above the mean.